How can I apply a modifier to a multi-user data object?
You can create a plain duplicate using ShiftD (instead of a Linked Duplicate).

Then apply the modifier on the duplicate. Now this unique mesh data will have the modifier applied to it.

After that, for any object that you want to use the modified mesh, just go to the Mesh Context and select it from the drop-down list.



In this example 'Cube.001' is the mesh with the modifier applied.